Problem Solving

Can someone please solve and explain this question to me

A cashier mentally reversed the digits of one customers correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 45 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?

A. 14
B. 45
C. 54
D. 65
E. 83

Thanks

We know that the correct amount and the actual amount will differ by 45 cents. So, just look at the answer choices, flip the digits, and find which one differs from the original by 45.

The correct answer is (E) since 83 and 38 differ by 45.

The other answers differ by other amounts. For example, (A) gives you 14 and 41, which differ by 27.

Fun question!

Let the two digits be x and y
So, the correct amount should have been 10x+y and the cashier gave out 10y+x
And we know that 10x+y-(10y+x)=45
10x+y-10y-x=45-->9x-9y=45-->9(x-y)=45-->x-y=5
So, the correct amount could have been 83 b/c 8-3=5